Homework #1

Due in class Friday September 5^th.

Problems from book

1. 1-3 This is quite straightforward so long as you visualise the geometry correctly.
2. 1-7 A little trivial vector practice. Please note that there are eight different diagonal vectors if you include the sign.
3. 1-10 Again, simple practice.
4. 1-18 Hint, how are cross-products related to triangle areas?
5. 1-24 I am especially interested in the answer to the question at the end.
6. 1-27 Calculus practice.
7. 1-33 More calculus practice.
8. 1-36 And still more. Don't forget about the flat surfaces closing the ends of the cylinder.
9. 1-38 This is clearly a case for Stoke's law. I will offer the direct evaluation, not using Stoke's law, as an challenge for extra credit.
10. 1-40 I did this math in 295, week 1 but that won't help most of you. Check the Schaum's Advanced Math book if you are rusty.
11. (Taken from Fowle's book) A fly moves in a spiral path according to the formula (in Cartesians)
    r(t) = (b sin(ωt), b cos(ωt), c t²)
    Show that the magnitude of the fly's acceleration is constant (assuming that b, c, and ω are constant).
12. (Courtesy of Seth.) A ball is kicked into the air with an initial speed of v₀ at and angle θ above the horizontal. If there is no air resistance then the ball follows a parabolic trajectory that you can all easily find. Derive an expression for the angle φ between the ground and the radius vector to the ball. Compare the maximum value of φ with the value of φ when the ball is at the maximum height above the ground. Would the value of φ at maximum height be the same if you repeated the computation for a ball on the moon?